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Linear FunctionEdit

For any 2 point A(0,0) , B( ) a straight line can be drawn . The slope of the line is

 

Therefore,

 

For a point C( ) on the same line of the slope m

 
 

Linear EquationsEdit

Has general form

   
   
   
    with  
  with  

System of Linear EquationsEdit

ExampleEdit

 
 

Roots of system of equationsEdit

Variable EliminationEdit

 
 

Multiply 1st row by 2 add to 2nd row

 
 

Yields

  =>  

Multiply 1st row by -3 add to 2nd row

 
 

Yields

  =>  

SubstitutionEdit

If you get a system of equations that looks like this:

 
 

You can switch around some terms in the first to get this:

 

Then you can substitute that into the bottom one so that it looks like this:

 
 
 
 
 

Then, you can substitute 2 into an x from either equation and solve for y. It's usually easier to substitute it in the one that had the single y. In this case, after substituting 2 for x, you would find that y = 7.

DeterminantEdit

If you get a system of equations that looks like this:

 
 

Solve for y

 
 
 
 

Solve for x

 
 
 
 

Find Roots of System of Linear Equations systematicallyEdit

 
 

Eliminate variable x

 
 

Add

 

Solve for y

 

Eliminate variable y

 
 

Add

 

Solve for x

 

ReferenceEdit

External linksEdit